Question

Following maintenance and calibration, an extrusion machine produces aluminum tubing with a mean outside diameter of 2.500 inches, with a standard deviation of 0.027 inches. As the machine functions over an extended number of work shifts, the standard deviation remains unchanged, but the combination of accumulated deposits and mechanical wear causes the mean diameter to “drift” away from the desired 2.500 inches. For a recent random sample of 34 tubes, the mean diameter was 2.509 inches. At the 0.01 level of significance, does the machine appear to be in need of maintenance and calibration? Assumed true population means of 2.495, 2.500, 2.505, 2.510, and 2.515 inches, plot the power curve

Answer 1

Given the following data in the question

Sample Mean = 2.509

Standard deviation = 0.027

Sample size = 34

Level of significance = 0.01

Hence

Null hypothesis, H0 : µ = 2.5

Alternative Hypothesis, Ha : µ ≠ 2.5

Now we will calculate the value of z

  

Now by looking the t-table the z value for the corresponding data value comes out to be 2.4448.

Now the calculated z value is smaller than the observed z value from the table. Hence we accept the null hypothesis. Which means the machine does not appears to in the need of calibration and maintenance.